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The 28-year-old is set to become Atletico's fourth signing of the summer, while Spurs will also retain a 15 per cent sell-on clause as part of the deal.
Argentina international Romero was the subject of interest from Premier League champions Arsenal in recent days, but Tottenham did not want to sell their captain to their north London rivals.
He leaves Tottenham after five seasons, having made 156 appearances for them, scoring 13 times, following an initial campaign on loan from Atalanta in 2021.
The centre-back played for Argentina during their run to the World Cup final this summer, missing just one game.
Romero was scheduled to return to pre-season with Spurs in the coming week after being given extra time off following the tournament in North America.
He captained the side last season as Tottenham narrowly avoided relegation from the Premier League.
Having signed permanently from Atalanta in a £42.5m deal, Romero became a key figure in their defence.
The news will be a blow to Spurs fans who are also set to lose Djed Spence to Inter Milan , who are in advanced talks to sign the England full-back in a £25.6m (30m euros) deal.
With the additions of midfielders Kang-in Lee and Morten Hjulmand and left-back Alejandro Grimaldo, Atletico are set to take their transfer spending over £100m this summer should they complete the Romero deal.
Head coach Diego Simeone is aiming to strengthen his squad after they finished fourth in La Liga last season, with Villarreal beating them to third place.
Inter in advanced talks for Spurs full-back Spence
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